Problem: Solve for $x$, $ \dfrac{3x + 4}{4x - 2} = \dfrac{4}{4x - 2} - \dfrac{10}{8x - 4} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4x - 2$ $4x - 2$ and $8x - 4$ The common denominator is $8x - 4$ To get $8x - 4$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{3x + 4}{4x - 2} \times \dfrac{2}{2} = \dfrac{6x + 8}{8x - 4} $ To get $8x - 4$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{4}{4x - 2} \times \dfrac{2}{2} = \dfrac{8}{8x - 4} $ The denominator of the third term is already $8x - 4$ , so we don't need to change it. This give us: $ \dfrac{6x + 8}{8x - 4} = \dfrac{8}{8x - 4} - \dfrac{10}{8x - 4} $ If we multiply both sides of the equation by $8x - 4$ , we get: $ 6x + 8 = 8 - 10$ $ 6x + 8 = -2$ $ 6x = -10 $ $ x = -\dfrac{5}{3}$